On approximation of the eigenvalues of perturbed periodic Schrödinger operators

Lyonell Boulton; Michael Levitin

doi:10.1088/1751-8113/40/31/010

On approximation of the eigenvalues of perturbed periodic Schrödinger operators

Lyonell Boulton, Michael Levitin

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrödinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so-called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples. © 2007 IOP Publishing Ltd.

Original language	English
Article number	010
Pages (from-to)	9319-9329
Number of pages	11
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	40
Issue number	31
DOIs	https://doi.org/10.1088/1751-8113/40/31/010
Publication status	Published - 27 Jul 2007

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abstract = "This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schr{\"o}dinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so-called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples. {\textcopyright} 2007 IOP Publishing Ltd.",

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AB - This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrödinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so-called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples. © 2007 IOP Publishing Ltd.

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On approximation of the eigenvalues of perturbed periodic Schrödinger operators

Abstract

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